In order to preserve integrability, the boundary potential has to satisfy the non-trivial constraint (REF ), which depends on the form of the bulk Lagrangian. Hence, for a given bulk Lagrangian, the integrability constraint restricts the form of the boundary Lagrangian. In fact, following the procedure of Ghoshal and Zamolodchikov for the sine-Gordon model [1]}, we have found that in the case of the bulk \(T\bar{T}\) -Lagrangian the existence of a higher conserved charge requires the boundary potential to be zero. Our results are summarized in Table REF .
<TABLE>